Omnibus Test Contours for Departures from Normality Based on √b 1 and b 2

Bowman, K. O.; Shenton, L. R.

doi:10.2307/2335355

Cited by 112 publications

(85 citation statements)

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“…In this example, there is a positive spatial autocorrelation in the explained variable (ρ = 0.5) and the variances of half of the samples are larger the than other half (Ω ii =ᾱ 0 +ᾱ 1 = 13 or Ω ii =ᾱ 0 = 1). The row of 'BS/JB Test' shows p-values of Bowman and Shenton (1975) (Jarque and Bera (1987)) normality test. In this example, the following points can be observed.…”

Section: Designmentioning

confidence: 99%

Efficient Maximum Likelihood Estimation of Spatial Autoregressive Models with Normal But Heteroskedastic Disturbances

Yokoi

2010

SSRN Journal

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. The likelihood functions for spatial autoregressive models with normal but heteroskedastic disturbances have been derived [Anselin (1988, ch.6)], but there is no implementation of maximum likelihood estimation for these likelihood functions in general cases with heteroskedastic disturbances. This is the reason why less efficient IV-based methods, 'robust 2-SLS' estimation for example, must be applied if disturbance terms might be heteroskedastic. In this paper, we develop a new computer program for maximum likelihood estimation and confirm the efficiency of our estimator in cases with heteroskedastic disturbances, using Monte Carlo simulations. Terms of use: Documents in EconStor may

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Section: Designmentioning

confidence: 99%

Efficient Maximum Likelihood Estimation of Spatial Autoregressive Models with Normal But Heteroskedastic Disturbances

Yokoi

2010

SSRN Journal

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“…Further, averages of two diagnostic statistics are reported together with the percentages of M diagnostics that have not passed the corresponding critical value. The first diagnostic test statistic is the normality test of Doornik and Hansen (1994), which is an adapted version of the test for normality of Bowman and Shenton (1975), and is χ 2 distributed with two degrees of freedom. The second diagnostic is the heteroskedasticity test…”

Section: Arma Simulation Resultsmentioning

confidence: 99%

Time Series Models with a Common Stochastic Variance for Analysing Economic Time Series

Koopman

Bos

2003

SSRN Journal

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The linear Gaussian state space model for which the common variance is treated as a stochastic time-varying variable is considered for the modelling of economic time series. The focus of this paper is on the simultaneous estimation of parameters related to the stochastic processes of the mean part and the variance part of the model. The estimation method is based on maximum likelihood and it requires the subsequent uses of the Kalman filter to treat the mean part and sampling techniques to treat the variance part. This approach leads to the evaluation of the exact likelihood function of the model subject to simulation error. The standard asymptotic properties of maximum likelihood estimators apply as a result. A Monte Carlo study is carried out to investigate the small-sample properties of the estimation procedure. We present two illustrations which are concerned with the modelling and forecasting of two U.S. macroeconomic time series: inflation and industrial production.

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“…It should be noted that the statistic was originally developed by Bowman and Shenton (1975). They, however, did not mention on the properties of the statistic such as large or finite sample properties.…”

Section: Jarque-bera Testmentioning

confidence: 99%

Comprehensive comparison of normality tests: Empirical study using many different types of data

Lee¹,

Park²,

Jeong³

2016

Journal of the Korean Data and Information Science Society

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We compare many normality tests consisting of different sources of information extracted from the given data: Anderson-Darling test, Kolmogorov-Smirnov test, Cramervon Mises test, Shapiro-Wilk test, Shaprio-Francia test, Lilliefors, Jarque-Bera test, D'Agostino' D, Doornik-Hansen test, Energy test and Martinzez-Iglewicz test. For the purpose of comparison, those tests are applied to the various types of data generated from skewed distribution, unsymmetric distribution, and distribution with different length of support. We then summarize comparison results in terms of two things: type I error control and power. The selection of the best test depends on the shape of the distribution of the data, implying that there is no test which is the most powerful for all distributions.Keywords: Empirical power, empirical type I error, limiting distribution, normality tests. IntroductionMany statistical methodologies, which have been developed so far, work very well under the assumption that the data come from normal distribution and it is very important to check for normality before any statistical analysis is done. Over several decades, various tests including goodness-of-fit test (Kang et al., 2014;Lee, 2013) using different sources of information from data have been introduced by many researchers. More specifically, some methods exploit sample skewness or/and sample kurtosis (D'Agostino, 1970;D'Agostino and Pearson, 1973;Jarque and Bera, 1981) while other methods use the maximum distance between two distribution functions, i.e., target normal distribution function and empirical distribution function (Kolmogorov, 1933;Lilliefors, 1967Lilliefors, , 1969Smirnov, 1939). Other than that, some method uses the ratio of two estimators of variance (Martinez and Iglewicz, 1981 (Anderson, 1962;Cramer, 1928;von Mises, 1928;Shapiro and Wilk, 1965;Shapiro and Francia, 1972;Lilliefors, 1967;Jarque and Bera, 1981;D'Agostino, 1970;Doornik and Hansen, 2008;Szekely and Rizzo, 2005;Martinez and Iglewicz, 1981). Since each method makes use of different type of information extracted from the given data, the performance of each method depends heavily on the properties of the data: skewness, kurtosis, and the type of support. Accordingly, it is well known that there is no test which is the most powerful for all types of alternatives. In order to compare such methods, we apply those tests to the data generated from many different distributions and then find the best test for each alternative.In this paper, we focus on the one sample test. That is, given the samples X 1 , · · · , X n , we test for the normality of the given sample of data. Furthermore, for simplicity, our interest is restricted to the univariate normal data.

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Omnibus Test Contours for Departures from Normality Based on √b 1 and b 2

Cited by 112 publications

References 1 publication

Efficient Maximum Likelihood Estimation of Spatial Autoregressive Models with Normal But Heteroskedastic Disturbances

Efficient Maximum Likelihood Estimation of Spatial Autoregressive Models with Normal But Heteroskedastic Disturbances

Time Series Models with a Common Stochastic Variance for Analysing Economic Time Series

Comprehensive comparison of normality tests: Empirical study using many different types of data

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